q-Schrodinger equations for V=u(2)+1/u(2) and Morse potentials in terms of the q-canonical transformation

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2, 1) of the Schrodinger equations for the Morse and the V = u(2) + 1/u(2) potentials were known to be related by a canonical transformation. q-deformed analog of this transformation connecting two different realizations of the sl(q)(2) algebra is presented. By the virtue of the q-canonical transformation, a q-deformed Schrodinger equation for the Morse potential is obtained from the q-deformed V = u(2)+1/u(2) Schrodinger equation. Wave functions and eigenvalues of the q-Schrodinger equations yielding a new definition of the q-Laguerre polynomials are studied.